M. B. Block D 4/11/09 Comparing and Scaling The Big Idea: Many important practical and mathematical applications involve comparing quantities of one kind or another; it is important to know which method to use and how we should use them. Investigation 2: Comparing by Finding Percents Essential Question: What methods are there for comparing things? 2.1
In the table above, look for interesting patters in the data for males and females and in the data for the two age groups. A Why don’t the numbers in the columns add up to the given totals?
I think that this is because one person can vote more than once but that does not change the total number of people. B Write three statements that use percents to make comparisons about the numbers of male and female participants in various activities. Explain how you found the percents.
1 In the biking activity the percent of males who bike was about 21.9% that beat the female age group in that activity because they only had 19.7% of the people who bike.
2 In the swimming activity the percent of females who swam was about 28.3% that beat the male age group in that activity because they only had 24.7% of the people swim.
3 In the fishing activity the percent of males who fish was about 27.2%that beat the female age group in that activity because they only had 12.5% of the people who fish.
The way I found out the percents was that I divided the number of people doing the activity by the total number of people. C Write three statements that use percents to make comparisons about number of teenage and older-adult participants in the various activities.
1 In the walking activity the percent of ages 55-64 who walk was 37.1% that outnumbers the ages 12-17 because they only have 13.2% of people who walk.
2 In the swimming activity the percent of ages 12-17 who swim was 51% that highly outnumbered the ages 55-64 because they only have 13.1% of people who swim.
3 In the biking activity the percent of ages 12-17 who bike was 41.2% that is higher than the ages 55-64 because they only have 9.7% of people who bike. D Write three statements that make comparisons about the data without using percents.
1 In the fishing activity the males who fish was 30,449,000 and the female and ages 12-17 and ages 55-64 together add up to 22,986,000 which is less than the males alone!
2 The total number of females (118,555,000) equals the total number of ages 12-17 (21,304,000) times 5.56491739.
3 In the walking activity the total number of females was 43,373,000 and the total number of people in ages 12-17 was 2,816,000. The big difference is 40,557,000. Follow up 1 Explain how you might decide when percents would be a good way to make a comparison and when other forms of comparison would be better. Use examples if they help explain your ideas.
Percents are better when you compare ratios. When you don’t want to compare ratios you can use other methods of comparing numbers not using percents. 2 Can you compare the participation of teenage boys in these activities to the participation of older-adult women by using the data in the table? Explain.
No because from the table I can’t tell how many teenagers are boys and how many are girls. Also in the males and females I don’t know their age.
Block D
4/11/09
Comparing and Scaling
The Big Idea:
Many important practical and mathematical applications involve comparing quantities of one kind or another; it is important to know which method to use and how we should use them.
Investigation 2: Comparing by Finding Percents
Essential Question:
What methods are there for comparing things?
2.1
A Why don’t the numbers in the columns add up to the given totals?
I think that this is because one person can vote more than once but that does not change the total number of people.
B Write three statements that use percents to make comparisons about the numbers of male and female participants in various activities. Explain how you found the percents.
1 In the biking activity the percent of males who bike was about 21.9% that beat the female age group in that activity because they only had 19.7% of the people who bike.
2 In the swimming activity the percent of females who swam was about 28.3% that beat the male age group in that activity because they only had 24.7% of the people swim.
3 In the fishing activity the percent of males who fish was about 27.2%that beat the female age group in that activity because they only had 12.5% of the people who fish.
The way I found out the percents was that I divided the number of people doing the activity by the total number of people.
C Write three statements that use percents to make comparisons about number of teenage and older-adult participants in the various activities.
1 In the walking activity the percent of ages 55-64 who walk was 37.1% that outnumbers the ages 12-17 because they only have 13.2% of people who walk.
2 In the swimming activity the percent of ages 12-17 who swim was 51% that highly outnumbered the ages 55-64 because they only have 13.1% of people who swim.
3 In the biking activity the percent of ages 12-17 who bike was 41.2% that is higher than the ages 55-64 because they only have 9.7% of people who bike.
D Write three statements that make comparisons about the data without using percents.
1 In the fishing activity the males who fish was 30,449,000 and the female and ages 12-17 and ages 55-64 together add up to 22,986,000 which is less than the males alone!
2 The total number of females (118,555,000) equals the total number of ages 12-17 (21,304,000) times 5.56491739.
3 In the walking activity the total number of females was 43,373,000 and the total number of people in ages 12-17 was 2,816,000. The big difference is 40,557,000.
Follow up
1 Explain how you might decide when percents would be a good way to make a comparison and when other forms of comparison would be better. Use examples if they help explain your ideas.
Percents are better when you compare ratios. When you don’t want to compare ratios you can use other methods of comparing numbers not using percents.
2 Can you compare the participation of teenage boys in these activities to the participation of older-adult women by using the data in the table? Explain.
No because from the table I can’t tell how many teenagers are boys and how many are girls. Also in the males and females I don’t know their age.